Optimal packings of bounded degree trees

@article{Joos2016OptimalPO,
  title={Optimal packings of bounded degree trees},
  author={Felix Joos and Jaehoon Kim and D. Kuhn and D. Osthus},
  journal={arXiv: Combinatorics},
  year={2016}
}
We prove that if $T_1,\dots, T_n$ is a sequence of bounded degree trees so that $T_i$ has $i$ vertices, then $K_n$ has a decomposition into $T_1,\dots, T_n$. This shows that the tree packing conjecture of Gyarfas and Lehel from 1976 holds for all bounded degree trees (in fact, we can allow the first $o(n)$ trees to have arbitrary degrees). Similarly, we show that Ringel's conjecture from 1963 holds for all bounded degree trees. We deduce these results from a more general theorem, which yields… Expand
A blow-up lemma for approximate decompositions
Tree decompositions of graphs without large bipartite holes
Packing trees of unbounded degrees in random graphs
A bandwidth theorem for approximate decompositions
Decomposing almost complete graphs by random trees
  • A. Lladó
  • Mathematics, Computer Science
  • Electron. Notes Discret. Math.
  • 2014
Packing large trees of consecutive orders
  • Andrzej Zak
  • Mathematics, Computer Science
  • Discret. Math.
  • 2017
A proof of Ringel's Conjecture
Perfectly packing graphs with bounded degeneracy and many leaves
Almost all trees are almost graceful
Decompositions of quasirandom hypergraphs into hypergraphs of bounded degree
...
1
2
3
...

References

SHOWING 1-10 OF 34 REFERENCES
A blow-up lemma for approximate decompositions
Packing large trees of consecutive orders
  • Andrzej Zak
  • Mathematics, Computer Science
  • Discret. Math.
  • 2017
Packing minor-closed families of graphs into complete graphs
Optimal path and cycle decompositions of dense quasirandom graphs
Hamilton decompositions of regular expanders: a proof of Kelly's conjecture for large tournaments
An approximate version of the tree packing conjecture
Packing Tree Factors in Random and Pseudo-random Graphs
On the Tree Packing Conjecture
A Fast Approximation Algorithm for Computing the Frequencies of Subgraphs in a Given Graph
Decomposing almost complete graphs by random trees
  • A. Lladó
  • Mathematics, Computer Science
  • J. Comb. Theory, Ser. A
  • 2018
...
1
2
3
4
...